Every Pokémon has a Nature you can see on their information screen, and this is something that comes into play in how its stats will grow over time. The Nature of a Pokémon can give you an instant read as to whether you should bother training a 'mon or popping them on the trade network .
The Natures, and their effects, are as follows:
|Rash||Sp. Attack||Sp. Defense|
|Careful||Sp. Defense||Sp. Attack|
As a rule of thumb an Increased Stat will add 10% to that statistic while a Decreased Stat will cause a 10% decrease . Nature’s are handed out at random when you catch or hatch a Pokémon. During the main quest, it honestly makes little difference what Nature your Pokemon has (or their stats, even).
However, when you're up against fellow players or the tougher post-game battles, having the right Nature can be very beneficial. For example, an Adamant nature for physical attacks. In which case, these two tricks can help you to find Pokemon with a certain Nature more easily.
In the wild, if you have a Pokemon with the Synchronize ability at the front, there's a 50% chance the wild Pokemon will have the same Nature as the Pokemon in front. This is useful for legendary encounters mainly.
When hatching eggs, if you have a parent hold onto the Everstone item, they will pass their Nature down 100% of the time. Better go and book the Daycare Centre ASAP then.